Coarse--graining and hints of scaling in a population of 1000+ neurons

TL;DR

This study applies coarse-graining techniques to large neuronal populations, revealing scale-invariant behaviors and fixed points, indicating complex collective dynamics akin to critical phenomena.

Contribution

It introduces explicit coarse-graining methods to neural data, demonstrating evidence of non-Gaussian fixed points and power-law dependencies in large neuronal networks.

Findings

Probability distributions approach a fixed non-Gaussian form

Evidence of power-law dependencies across scales

Indications of a non-trivial fixed point in neural activity

Abstract

In many systems we can describe emergent macroscopic behaviors, quantitatively, using models that are much simpler than the underlying microscopic interactions; we understand the success of this simplification through the renormalization group. Could similar simplifications succeed in complex biological systems? We develop explicit coarse-graining procedures that we apply to experimental data on the electrical activity in large populations of neurons in the mouse hippocampus. Probability distributions of coarse-grained variables seem to approach a fixed non-Gaussian form, and we see evidence of power-law dependencies in both static and dynamic quantities as we vary the coarse-graining scale over two decades. Taken together, these results suggest that the collective behavior of the network is described by a non-trivial fixed point.